Peanuts are legumes, not nuts, so generally they are not considered paleo. You can read about why this is here, in this excellent article:
http://whole9life.com/2009/12/peanut-manifesto/
Excerpt:
It’s not the ingredients in the peanut butter we don’t like, it’s the peanuts themselves. When peanuts grow, they can harbor carcinogenic mold called an “aflatoxin“. This goes for conventional and organic peanuts. They The longer they sit (during shipping, for example), especially in warm temperatures and high humidity, the more mold grows. And as it’s nearly impossible to buy peanuts “local”, as they are only grown in a few Southern locations, more likely than not that even your organic peanuts are suspect.
The far bigger concern, however, is that peanuts contain lectins which are believed to have inflammatory and atherogenic potential. Most plants contain lectins, some of which are toxic, inflammatory, or both. Many of these lectins are resistant to cooking and to digestive enzymes, and some have been scientifically shown to have significant GI toxicity in humans. Lectins from grains (especially wheat) and legumes (including peanuts and soybeans) are most commonly associated with aggravation of inflammatory and digestive diseases in the body. (As an aside, dairy from cows fed grain-based diets can also contain these grain-derived lectins.)